Fluorescence interference contrast microscopy

Fluorescence interference contrast (FLIC) microscopy is a microscopic technique developed to achieve z-resolution on the nanometer scale.

FLIC occurs whenever fluorescent objects are in the vicinity of a reflecting surface (e.g. Si wafer). The resulting interference between the direct and the reflected light leads to a double sin2 modulation of the intensity, I, of a fluorescent object as a function of distance, h, above the reflecting surface. This allows for the nanometer height measurements.

FLIC microscope is well suited to measuring the topography of a membrane that contains fluorescent
probes e.g. an artificial lipid bilayer, or a living cell membrane or the structure of fluorescently labeled proteins on a surface.

Contents

The optical theory underlying FLIC was developed by Armin Lambacher and Peter Fromherz. They derived a relationship between the observed fluorescence intensity and the distance of the fluorophore from a reflective silicon surface.

The observed fluorescence intensity, IFLIC{\displaystyle I_{FLIC}}, is the product of the excitation probability per unit time, Pex{\displaystyle P_{ex}}, and the probability of measuring an emitted photon per unit time, Pem{\displaystyle P_{em}}. Both probabilities are a function of the fluorophore height above the silicon surface, so the observed intensity will also be a function of the fluorophore height. The simplest arrangement to consider is a fluorophore embedded in silicon dioxide (refractive index n1{\displaystyle n_{1}}) a distance d from an interface with silicon (refractive index n0{\displaystyle n_{0}}). The fluorophore is excited by light of wavelength λex{\displaystyle \lambda _{ex}} and emits light of wavelength λem{\displaystyle \lambda _{em}}. The unit vector ″eex″{\displaystyle ''e_{ex}''} gives the orientation of the transition dipole of excitation of the fluorophore. Pex{\displaystyle P_{ex}} is proportional to the squared projection of the local electric field, Fin{\displaystyle F_{in}}, which includes the effects of interference, on the direction of the transition dipole.
Pex∝∣Fin⋅eex∣2{\displaystyle P_{ex}\propto \mid F_{in}\cdot e_{ex}\mid ^{2}}
The local electric field, Fin{\displaystyle F_{in}}, at the fluorophore is affected by interference between the direct incident light and the light reflecting off the silicon surface. The interference is quantified by the phase difference Φin{\displaystyle \Phi _{in}} given by
Φin=4πn1dcos⁡θ1inλex{\displaystyle \Phi _{in}={\frac {4\pi n_{1}d\cos \theta _{1}^{in}}{\lambda _{ex}}}}θ1in{\displaystyle \theta _{1}^{in}} is the angle of the incident light with respect to the silicon plane normal. Not only does interference modulate Fin{\displaystyle F_{in}}, but the silicon surface does not perfectly reflect the incident light. Fresnel coefficients give the change in amplitude between an incident and reflected wave. The Fresnel coefficients depend on the angles of incidence, θi{\displaystyle \theta _{i}} and θj{\displaystyle \theta _{j}}, the indices of refraction of the two mediums and the polarization direction. The angles θi{\displaystyle \theta _{i}} and θj{\displaystyle \theta _{j}} can be related by Snell's Law. The expressions for the reflection coefficients are:
rijTE=nicos⁡θi−njcos⁡θjnicos⁡θi+njcos⁡θjrijTM=njcos⁡θi−nicos⁡θjnjcos⁡θi+nicos⁡θj{\displaystyle r_{ij}^{TE}={\frac {n_{i}\cos \theta _{i}-n_{j}\cos \theta _{j}}{n_{i}\cos \theta _{i}+n_{j}\cos \theta _{j}}}\quad r_{ij}^{TM}={\frac {n_{j}\cos \theta _{i}-n_{i}\cos \theta _{j}}{n_{j}\cos \theta _{i}+n_{i}\cos \theta _{j}}}}
TE refers to the component of the electric field perpendicular to the plane of incidence and TM to the parallel component (The incident plane is defined by the plane normal and the propagation direction of the light). In cartesian coordinates, the local electric field is
Fin=sin⁡γin[01+r10TEeiΦin0]+cos⁡γin[cos⁡θ1in(1−r10TMeiΦin)0sin⁡θ1in(1+r10TMeiΦin)]{\displaystyle F_{in}=\sin \gamma _{in}\left[{\begin{array}{c}0\\1+r_{10}^{TE}{\textit {e}}^{i\Phi _{in}}\\0\end{array}}\right]+\cos \gamma _{in}\left[{\begin{array}{c}\cos \theta _{1}^{in}(1-r_{10}^{TM}{\textit {e}}^{i\Phi _{in}})\\0\\\sin \theta _{1}^{in}(1+r_{10}^{TM}{\textit {e}}^{i\Phi _{in}})\end{array}}\right]}γin{\displaystyle \gamma _{in}} is the polarization angle of the incident light with respect to the plane of incidence. The orientation of the excitation dipole is a function of its angle θex{\displaystyle \theta _{ex}} to the normal and ϕex{\displaystyle \phi _{ex}} azimuthal to the plane of incidence.
eex=[cos⁡ϕexsin⁡θexsin⁡ϕexsin⁡θexcos⁡θex]{\displaystyle {\textit {e}}_{ex}=\left[{\begin{array}{c}\cos \phi _{ex}\sin \theta _{ex}\\\sin \phi _{ex}\sin \theta _{ex}\\\cos \theta _{ex}\end{array}}\right]}
The above two equations for Fin{\displaystyle F_{in}} and eex{\displaystyle {\textit {e}}_{ex}} can be combined to give the probability of exciting the fluorophore per unit time Pex{\displaystyle P_{ex}}.
Many of the parameters used above would vary in a normal experiment. The variation in the five following parameters should be included in this theoretical description.

Example of a FLIC intensity plot showing the relative fluorescence intensity measured versus the distance of the fluorophore from the reflective surface. The peaks might not be the same height in a real experimental plot

Normalization factors are not included. O(θex){\displaystyle O(\theta _{ex})} is a distribution of the orientation angle of the fluorophore dipoles. The azimuthal angle ϕex{\displaystyle \phi _{ex}} and the polarization angle γin{\displaystyle \gamma _{in}} are integrated over analytically, so they no longer appear in the above equation. To finally obtain the probability of excitation per unit time, the above equation is integrated over the spread in excitation wavelength, accounting for the intensity I(λex){\displaystyle I(\lambda _{ex})} and the extinction coefficient of the fluorophore ϵ(λex){\displaystyle \epsilon (\lambda _{ex})}.
Pex∝∫dλexI(λex)ϵ(λex)<∣Fin⋅eex∣2>{\displaystyle P_{ex}\propto \int d\lambda _{ex}I(\lambda _{ex})\epsilon (\lambda _{ex})<\mid F_{in}\cdot e_{ex}\mid ^{2}>}
The steps to calculate Pem{\displaystyle P_{em}} are equivalent to those above in calculating Pex{\displaystyle P_{ex}} except that the parameter labels em are replaced with ex and in is replaced with out.Pem∝∫dλemΦdet(λem)f(λem)<∣Fin⋅eex∣2>{\displaystyle P_{em}\propto \int d\lambda _{em}\Phi _{det}(\lambda _{em}){\textit {f}}(\lambda _{em})<\mid F_{in}\cdot e_{ex}\mid ^{2}>}
The resulting fluorescence intensity measured is proportional to the product of the excitation probability and emission probability

IFLIC∝PexPem{\displaystyle I_{FLIC}\propto P_{ex}P_{em}}
It is important to note that this theory determines a proportionality relation between the measured fluorescence intensity IFLIC{\displaystyle I_{FLIC}} and the distance of the fluorophore above the reflective surface. The fact that it is not an equality relation will have a significant effect on the experimental procedure.

A silicon wafer is typically used as the reflective surface in a FLIC experiment. An oxide layer is then thermally grown on top of the silicon wafer to act as a spacer. On top of the oxide is placed the fluorescently labeled specimen, such as a lipid membrane, a cell or membrane bound proteins.
With the sample system built, all that is needed is an epifluorescence microscope and a CCD camera to make quantitative intensity measurements.

This is a diagram of an example FLIC experimental setup with silicon, three oxide layers and a fluorescently labeled lipid bilayer (the yellow stars represent fluorophores.

The silicon dioxide thickness is very important in making accurate FLIC measurements. As mentioned before, the theoretical model describes the relative fluorescence intensity measured versus the fluorophore height. The fluorophore position cannot be simply read off of a single measured FLIC curve. The basic procedure is to manufacture the oxide layer with at least two known thicknesses (the layer can be made with photolithographic techniques and the thickness measured by ellipsometry). The thicknesses used depends on the sample being measured. For a sample with fluorophore height in the range of 10 nm, oxide thickness around 50 nm would be best because the FLIC intensity curve is steepest here and would produce the greatest contrast between fluorophore heights. Oxide thickness above a few hundred nanometers could be problematic because the curve begins to get smeared out by polychromatic light and a range of incident angles. A ratio of measured fluorescence intensities at different oxide thicknesses is compared to the predicted ratio to calculate the fluorophore height above the oxide (df,{\displaystyle d_{\textit {f}},}).
Itheory(d1)Itheory(d0)=Iexp(d1+df)Iexp(d0+df){\displaystyle {\frac {I_{theory}(d_{1})}{I_{theory}(d_{0})}}={\frac {I_{exp}(d_{1}+d_{\textit {f}})}{I_{exp}(d_{0}+d_{\textit {f}})}}}
The above equation can then be solved numerically to find df{\displaystyle d_{\textit {f}}}.
Imperfections of the experiment, such as imperfect reflection, nonnormal incidence of light and polychromatic light tend to smear out the sharp fluorescence curves. The spread in incidence angle can be controlled by the numerical aperture (N.A.). However, depending on the numerical aperture used, the experiment will yield good lateral resolution (x-y) or good vertical resolution (z), but not both. A high N.A. (~1.0) gives good lateral resolution which is best if the goal is to determine long range topography. Low N.A. (~0.001), on the other hand, provides accurate z-height measurement to determine the height of a fluorescently labeled molecule in a system.

Example of experimental data collected for a fluorescently labeled sample over 16 oxide thicknesses. Fitting the curve to the 16 data points would give the height of the fluorophores above the oxide surface.

The basic analysis involves fitting the intensity data with the theoretical model allowing the distance of the fluorophore above the oxide surface (df{\displaystyle d_{\textit {f}}}) to be a free parameter.
The FLIC curves shift to the left as the distance of the fluorophore above the oxide increases. df{\displaystyle d_{\textit {f}}} is usually the parameter of interest, but several other free parameters are often included to optimize the fit. Normally an amplitude factor (a) and a constant additive term for the background (b) are included. The amplitude factor scales the relative model intensity and the constant background shifts the curve up or down to account for fluorescence coming from out of focus areas, such as the top side of a cell. Occasionally the numerical aperture (N.A.) of the microscope is allowed to be a free parameter in the fitting. The other parameters entering the optical theory, such as different indices of refraction, layer thicknesses and light wavelengths, are assumed constant with some uncertainty.
A FLIC chip may be made with oxide terraces of 9 or 16 different heights arranged in blocks. After a fluorescence image is captured, each 9 or 16 terrace block yields a separate FLIC curve that defines a unique df{\displaystyle d_{\textit {f}}}. The average df{\displaystyle d_{\textit {f}}} is found by compiling all the df{\displaystyle d_{\textit {f}}} values into a histogram.
The statistical error in the calculation of df{\displaystyle d_{\textit {f}}} comes from two sources: the error in fitting of the optical theory to the data and the uncertainty in the thickness of the oxide layer. Systematic error comes from three sources: the measurement of the oxide thickness (usually by ellipsometer), the fluorescence intensity measurement with the CCD, and the uncertainty in the parameters used in the optical theory. The systematic error has been estimated to be ∼1nm{\displaystyle \sim 1nm}.